Alligation Or Mixture

Question:
How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg?

[A].

36 kg

[B].

42 kg

[C].

54 kg

[D].

63 kg

Answer: Option D

Explanation:

S.P. of 1 kg of mixture = Rs. 9.24, Gain 10%.

C.P. of 1 kg of mixture = Rs.		100	x 9.24		= Rs. 8.40
		110

By the rule of allilation, we have:

C.P. of 1 kg sugar of 1st kind Cost of 1 kg sugar of 2nd kind
Rs. 9	Mean Price Rs. 8.40	Rs. 7
1.40		0.60

Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.

Let x kg of sugar of 1st be mixed with 27 kg of 2nd kind.

Then, 7 : 3 = x : 27

x =		7 x 27		= 63 kg.
		3

The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is:

[A].

Rs. 18

[B].

Rs. 18.50

[C].

Rs. 19

[D].

Rs. 19.50

Answer: Option A

Explanation:

Let the price of the mixed variety be Rs. x per kg.

By rule of alligation, we have:

Cost of 1 kg of Type 1 rice Cost of 1 kg of Type 2 rice
Rs. 15	Mean Price Rs. x	Rs. 20
(20 – x)		(x – 15)

	(20 – x)	=	2
	(x – 15)		3

60 – 3x = 2x – 30

5x = 90

x = 18.

Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.

[A].

1 : 3

[B].

2 : 3

[C].

3 : 4

[D].

4 : 5

Answer: Option B

Explanation:

By the rule of alligation:

Cost of 1 kg of 1st kind Cost of 1 kg of 2nd kind
720 p	Mean Price 630 p	570 p
60		90

Required ratio = 60 : 90 = 2 : 3.

In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?

[A].
3 : 7
[B].

5 : 7
[C].

7 : 3
[D].

7 : 5 

Answer: Option C

Explanation:

By the rule of alligation:

Cost of 1 kg pulses of 1st kind Cost of 1 kg pulses of 2nd kind
Rs. 15	Mean Price Rs. 16.50	Rs. 20
3.50		1.50

Required rate = 3.50 : 1.50 = 7 : 3.